Wenger is renowned for his reluctance to spend big on new recruits, with balancing the books as important to the Emirates boss as generating results on the field.
He is, however, aware of the need to strengthen during the winter window, helping to appease a disgruntled fan base, and has admitted that Cavani and Zaha are among those currently under consideration.
Wenger said: "Cavani is a player that I like.
"Will he cost a lot of money? That’s for sure. Nobody would deny that. Our banker lives just next to me at the moment and he is ready if we find the right player."
On Zaha, who is also a target for Manchester United, he added: "We are looking at him, but at the moment we have not made any bid for him.
"I don’t know if Manchester United are in for him. Anyway, if you call any club for any player, they will tell you Man United, Milan, Real Madrid are as well in for him, but it is always difficult to know if it is true or not."
Wenger is prepared to be patient in his pursuit of fresh faces, with it is opinion that it is often best to wait until the end of the window before making a move.
He said: "The prices always go up at the start of the transfer market and go down in the last week.
"Sometimes as well they go up in the last week, but it depends. Most of the time they go down in the last week and you know as well that 90 per cent of transfer activity happens in the last week, if not in the last 48 hours."